A large number of PSA cycles used for the separation of a composite gas mixture comprise an elution step and/or a recompression step using a gas fraction enriched with respect to the least adsorbable constituent of the initial gas flow extracted from the adsorber during a depressurization step. Examples are found, for example for the production of hydrogen, in the document U.S. Pat. No. 4,512,779 or, for the production of oxygen, in the document EP-A-0,743,087, both being in the name of the Applicant Company. Since the gas fraction used for elution and/or recompression is produced with a composition that is progressively less and less rich with respect to the least adsorbable constituent during the abovementioned decompression step, it is advantageous to store this fraction in a reservoir, making it possible to maintain the corresponding composition gradient in order subsequently to reinject the gas fraction into the adsorbent, this time with increasing purity. Examples of longitudinal-segregation vessels are described, for example, in the documents U.S. Pat. No. 4,512,779, which was mentioned above, EP-A-0,513,746 (Toyo) or U.S. Pat. No. 5,565,018 (Praxair). These documents describe intricate or expensive reservoir structures, with internal linings and/or dimensions which cannot be used on an industrial scale.